Quantum Mechanics of a Rotating Billiard

Abstract

Integrability of a square billiard is spontaneously broken as it rotates about one of its corners. The system becomes quasi-integrable where the invariant tori are broken with respect to a certain parameter, $λ= 2E/ω^{2}$ where E is the energy of the particle inside the billiard and $ω$ is the angular frequency of rotation of billiard. We study the system classically and quantum mechanically in view of obtaining a correspondence in the two descriptions. Classical phase space in Poincaré surface of section shows transition from regular to chaotic motion as the parameter $λ$ is decreased. In the Quantum counterpart, the spectral statistics shows a transition from Poisson to Wigner distribution as the system turns chaotic with decrease in $λ$. The wavefunction statistics however show breakdown of time-reversal symmetry as $λ$ decreases.